LMFDB - Embedded newform 115.2.e.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(22,115)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 $ x^20 - 6x^18 + 3x^16 + 80x^14 - 600x^12 + 3500x^10 - 15000x^8 + 50000x^6 + 46875x^4 - 2343750*x^2 + 9765625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.2
Root			$1.76871 + 1.36809i$ of defining polynomial
Character	$\chi$	$=$	115.22
Dual form			115.2.e.a.68.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68447 - 1.68447i) q^{2} +(-0.639677 + 0.639677i) q^{3} +3.67489i q^{4} +(1.36809 + 1.76871i) q^{5} +2.15503 q^{6} +(2.98466 - 2.98466i) q^{7} +(2.82130 - 2.82130i) q^{8} +2.18163i q^{9} +O(q^{10})$	\(q+(-1.68447 - 1.68447i) q^{2} +(-0.639677 + 0.639677i) q^{3} +3.67489i q^{4} +(1.36809 + 1.76871i) q^{5} +2.15503 q^{6} +(2.98466 - 2.98466i) q^{7} +(2.82130 - 2.82130i) q^{8} +2.18163i q^{9} +(0.674828 - 5.28385i) q^{10} -0.873996i q^{11} +(-2.35074 - 2.35074i) q^{12} +(0.853585 - 0.853585i) q^{13} -10.0552 q^{14} +(-2.00654 - 0.256265i) q^{15} -2.15503 q^{16} +(0.638446 - 0.638446i) q^{17} +(3.67489 - 3.67489i) q^{18} +7.03028 q^{19} +(-6.49981 + 5.02758i) q^{20} +3.81844i q^{21} +(-1.47222 + 1.47222i) q^{22} +(-1.52277 + 4.54766i) q^{23} +3.60945i q^{24} +(-1.25665 + 4.83951i) q^{25} -2.87568 q^{26} +(-3.31457 - 3.31457i) q^{27} +(10.9683 + 10.9683i) q^{28} -3.27366i q^{29} +(2.94828 + 3.81163i) q^{30} -0.332539 q^{31} +(-2.01251 - 2.01251i) q^{32} +(0.559075 + 0.559075i) q^{33} -2.15089 q^{34} +(9.36229 + 1.19571i) q^{35} -8.01724 q^{36} +(-6.19651 + 6.19651i) q^{37} +(-11.8423 - 11.8423i) q^{38} +1.09204i q^{39} +(8.84986 + 1.13026i) q^{40} -8.34978 q^{41} +(6.43206 - 6.43206i) q^{42} +(-5.55806 - 5.55806i) q^{43} +3.21184 q^{44} +(-3.85866 + 2.98466i) q^{45} +(10.2255 - 5.09533i) q^{46} +(5.25569 + 5.25569i) q^{47} +(1.37853 - 1.37853i) q^{48} -10.8164i q^{49} +(10.2688 - 6.03521i) q^{50} +0.816798i q^{51} +(3.13683 + 3.13683i) q^{52} +(-2.66974 - 2.66974i) q^{53} +11.1666i q^{54} +(1.54584 - 1.19571i) q^{55} -16.8413i q^{56} +(-4.49711 + 4.49711i) q^{57} +(-5.51440 + 5.51440i) q^{58} -5.93299i q^{59} +(0.941746 - 7.37380i) q^{60} -7.66012i q^{61} +(0.560153 + 0.560153i) q^{62} +(6.51143 + 6.51143i) q^{63} +11.0901i q^{64} +(2.67753 + 0.341961i) q^{65} -1.88349i q^{66} +(7.07050 - 7.07050i) q^{67} +(2.34622 + 2.34622i) q^{68} +(-1.93495 - 3.88311i) q^{69} +(-13.7564 - 17.7847i) q^{70} +4.12520 q^{71} +(6.15503 + 6.15503i) q^{72} +(-6.24912 + 6.24912i) q^{73} +20.8757 q^{74} +(-2.29187 - 3.89957i) q^{75} +25.8355i q^{76} +(-2.60859 - 2.60859i) q^{77} +(1.83951 - 1.83951i) q^{78} -14.9063 q^{79} +(-2.94828 - 3.81163i) q^{80} -2.30438 q^{81} +(14.0650 + 14.0650i) q^{82} +(-4.45689 - 4.45689i) q^{83} -14.0323 q^{84} +(2.00268 + 0.255772i) q^{85} +18.7248i q^{86} +(2.09409 + 2.09409i) q^{87} +(-2.46581 - 2.46581i) q^{88} +4.90838 q^{89} +(11.5274 + 1.47222i) q^{90} -5.09533i q^{91} +(-16.7121 - 5.59601i) q^{92} +(0.212718 - 0.212718i) q^{93} -17.7061i q^{94} +(9.61807 + 12.4345i) q^{95} +2.57472 q^{96} +(-8.21920 + 8.21920i) q^{97} +(-18.2200 + 18.2200i) q^{98} +1.90673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.68447	−	1.68447i	−1.19110	−	1.19110i	−0.976758	−	0.214343i	$-0.931239\pi$
$2$	−1.68447	−	1.68447i	−1.19110	−	1.19110i	−0.214343	−	0.976758i	$-0.568761\pi$
$3$	−0.639677	+	0.639677i	−0.369318	+	0.369318i	−0.867228	−	0.497911i	$-0.834101\pi$
$3$	−0.639677	+	0.639677i	−0.369318	+	0.369318i	0.497911	+	0.867228i	$0.334101\pi$
$4$			3.67489i			1.83744i
$5$	1.36809	+	1.76871i	0.611829	+	0.790990i
$5$	1.36809	+	1.76871i	0.611829	+	0.790990i
$6$	2.15503			0.879789
$7$	2.98466	−	2.98466i	1.12810	−	1.12810i	0.137611	−	0.990486i	$-0.456058\pi$
$7$	2.98466	−	2.98466i	1.12810	−	1.12810i	0.990486	−	0.137611i	$-0.0439424\pi$
$8$	2.82130	−	2.82130i	0.997482	−	0.997482i
$9$			2.18163i			0.727209i
$10$	0.674828	−	5.28385i	0.213399	−	1.67090i
$11$		−	0.873996i		−	0.263520i	−0.991282	−	0.131760i	$-0.957937\pi$
$11$		−	0.873996i		−	0.263520i	0.991282	−	0.131760i	$-0.0420628\pi$
$12$	−2.35074	−	2.35074i	−0.678601	−	0.678601i
$13$	0.853585	−	0.853585i	0.236742	−	0.236742i	−0.578758	−	0.815500i	$-0.696462\pi$
$13$	0.853585	−	0.853585i	0.236742	−	0.236742i	0.815500	+	0.578758i	$0.196462\pi$
$14$	−10.0552			−2.68736
$15$	−2.00654	−	0.256265i	−0.518086	−	0.0661674i
$16$	−2.15503			−0.538759
$17$	0.638446	−	0.638446i	0.154846	−	0.154846i	−0.625432	−	0.780278i	$-0.715077\pi$
$17$	0.638446	−	0.638446i	0.154846	−	0.154846i	0.780278	+	0.625432i	$0.215077\pi$
$18$	3.67489	−	3.67489i	0.866180	−	0.866180i
$19$	7.03028			1.61286			0.806429	−	0.591331i	$-0.201397\pi$
$19$	7.03028			1.61286			0.806429	+	0.591331i	$0.201397\pi$
$20$	−6.49981	+	5.02758i	−1.45340	+	1.12420i
$21$			3.81844i			0.833252i
$22$	−1.47222	+	1.47222i	−0.313879	+	0.313879i
$23$	−1.52277	+	4.54766i	−0.317520	+	0.948252i
$23$	−1.52277	+	4.54766i	−0.317520	+	0.948252i
$24$			3.60945i			0.736775i
$25$	−1.25665	+	4.83951i	−0.251331	+	0.967901i
$26$	−2.87568			−0.563967
$27$	−3.31457	−	3.31457i	−0.637889	−	0.637889i
$28$	10.9683	+	10.9683i	2.07282	+	2.07282i
$29$		−	3.27366i		−	0.607904i	−0.952687	−	0.303952i	$-0.901694\pi$
$29$		−	3.27366i		−	0.607904i	0.952687	−	0.303952i	$-0.0983063\pi$
$30$	2.94828	+	3.81163i	0.538280	+	0.695905i
$31$	−0.332539			−0.0597258			−0.0298629	−	0.999554i	$-0.509507\pi$
$31$	−0.332539			−0.0597258			−0.0298629	+	0.999554i	$0.509507\pi$
$32$	−2.01251	−	2.01251i	−0.355766	−	0.355766i
$33$	0.559075	+	0.559075i	0.0973225	+	0.0973225i
$34$	−2.15089			−0.368874
$35$	9.36229	+	1.19571i	1.58252	+	0.202111i
$36$	−8.01724			−1.33621
$37$	−6.19651	+	6.19651i	−1.01870	+	1.01870i	−0.0188774	+	0.999822i	$0.506009\pi$
$37$	−6.19651	+	6.19651i	−1.01870	+	1.01870i	−0.999822	+	0.0188774i	$0.993991\pi$
$38$	−11.8423	−	11.8423i	−1.92108	−	1.92108i
$39$			1.09204i			0.174866i
$40$	8.84986	+	1.13026i	1.39929	+	0.178710i
$41$	−8.34978			−1.30402			−0.652008	−	0.758212i	$-0.726073\pi$
$41$	−8.34978			−1.30402			−0.652008	+	0.758212i	$0.726073\pi$
$42$	6.43206	−	6.43206i	0.992488	−	0.992488i
$43$	−5.55806	−	5.55806i	−0.847596	−	0.847596i	0.142237	−	0.989833i	$-0.454571\pi$
$43$	−5.55806	−	5.55806i	−0.847596	−	0.847596i	−0.989833	+	0.142237i	$0.954571\pi$
$44$	3.21184			0.484203
$45$	−3.85866	+	2.98466i	−0.575215	+	0.444928i
$46$	10.2255	−	5.09533i	1.50766	−	0.751266i
$47$	5.25569	+	5.25569i	0.766621	+	0.766621i	0.977510	−	0.210889i	$-0.0676357\pi$
$47$	5.25569	+	5.25569i	0.766621	+	0.766621i	−0.210889	+	0.977510i	$0.567636\pi$
$48$	1.37853	−	1.37853i	0.198973	−	0.198973i
$49$		−	10.8164i		−	1.54521i
$50$	10.2688	−	6.03521i	1.45223	−	0.853508i
$51$			0.816798i			0.114375i
$52$	3.13683	+	3.13683i	0.435000	+	0.435000i
$53$	−2.66974	−	2.66974i	−0.366717	−	0.366717i	0.499561	−	0.866279i	$-0.333495\pi$
$53$	−2.66974	−	2.66974i	−0.366717	−	0.366717i	−0.866279	+	0.499561i	$0.833495\pi$
$54$			11.1666i			1.51958i
$55$	1.54584	−	1.19571i	0.208442	−	0.161229i
$56$		−	16.8413i		−	2.25051i
$57$	−4.49711	+	4.49711i	−0.595656	+	0.595656i
$58$	−5.51440	+	5.51440i	−0.724076	+	0.724076i
$59$		−	5.93299i		−	0.772409i	−0.922413	−	0.386205i	$-0.873786\pi$
$59$		−	5.93299i		−	0.772409i	0.922413	−	0.386205i	$-0.126214\pi$
$60$	0.941746	−	7.37380i	0.121579	−	0.951954i
$61$		−	7.66012i		−	0.980778i	−0.871504	−	0.490389i	$-0.836855\pi$
$61$		−	7.66012i		−	0.980778i	0.871504	−	0.490389i	$-0.163145\pi$
$62$	0.560153	+	0.560153i	0.0711395	+	0.0711395i
$63$	6.51143	+	6.51143i	0.820363	+	0.820363i
$64$			11.0901i			1.38626i
$65$	2.67753	+	0.341961i	0.332106	+	0.0424150i
$66$		−	1.88349i		−	0.231842i
$67$	7.07050	−	7.07050i	0.863799	−	0.863799i	−0.127978	−	0.991777i	$-0.540849\pi$
$67$	7.07050	−	7.07050i	0.863799	−	0.863799i	0.991777	+	0.127978i	$0.0408486\pi$
$68$	2.34622	+	2.34622i	0.284521	+	0.284521i
$69$	−1.93495	−	3.88311i	−0.232940	−	0.467472i
$70$	−13.7564	−	17.7847i	−1.64420	−	2.12567i
$71$	4.12520			0.489571			0.244786	−	0.969577i	$-0.421282\pi$
$71$	4.12520			0.489571			0.244786	+	0.969577i	$0.421282\pi$
$72$	6.15503	+	6.15503i	0.725378	+	0.725378i
$73$	−6.24912	+	6.24912i	−0.731404	+	0.731404i	−0.970898	−	0.239494i	$-0.923019\pi$
$73$	−6.24912	+	6.24912i	−0.731404	+	0.731404i	0.239494	+	0.970898i	$0.423019\pi$
$74$	20.8757			2.42675
$75$	−2.29187	−	3.89957i	−0.264642	−	0.450284i
$76$			25.8355i			2.96354i
$77$	−2.60859	−	2.60859i	−0.297276	−	0.297276i
$78$	1.83951	−	1.83951i	0.208283	−	0.208283i
$79$	−14.9063			−1.67709			−0.838547	−	0.544829i	$-0.816595\pi$
$79$	−14.9063			−1.67709			−0.838547	+	0.544829i	$0.816595\pi$
$80$	−2.94828	−	3.81163i	−0.329628	−	0.426153i
$81$	−2.30438			−0.256042
$82$	14.0650	+	14.0650i	1.55322	+	1.55322i
$83$	−4.45689	−	4.45689i	−0.489207	−	0.489207i	0.418849	−	0.908056i	$-0.362434\pi$
$83$	−4.45689	−	4.45689i	−0.489207	−	0.489207i	−0.908056	+	0.418849i	$0.862434\pi$
$84$	−14.0323			−1.53105
$85$	2.00268	+	0.255772i	0.217221	+	0.0277424i
$86$			18.7248i			2.01915i
$87$	2.09409	+	2.09409i	0.224510	+	0.224510i
$88$	−2.46581	−	2.46581i	−0.262856	−	0.262856i
$89$	4.90838			0.520287			0.260143	−	0.965570i	$-0.416230\pi$
$89$	4.90838			0.520287			0.260143	+	0.965570i	$0.416230\pi$
$90$	11.5274	+	1.47222i	1.21509	+	0.155186i
$91$		−	5.09533i		−	0.534136i
$92$	−16.7121	−	5.59601i	−1.74236	−	0.583425i
$93$	0.212718	−	0.212718i	0.0220578	−	0.0220578i
$94$		−	17.7061i		−	1.82625i
$95$	9.61807	+	12.4345i	0.986793	+	1.27575i
$96$	2.57472			0.262781
$97$	−8.21920	+	8.21920i	−0.834533	+	0.834533i	−0.988133	−	0.153600i	$-0.950913\pi$
$97$	−8.21920	+	8.21920i	−0.834533	+	0.834533i	0.153600	+	0.988133i	$0.450913\pi$
$98$	−18.2200	+	18.2200i	−1.84050	+	1.84050i
$99$	1.90673			0.191634
$100$	−17.7847	−	4.61807i	−1.77847	−	0.461807i
$101$	−0.253977			−0.0252717			−0.0126358	−	0.999920i	$-0.504022\pi$
$101$	−0.253977			−0.0252717			−0.0126358	+	0.999920i	$0.504022\pi$
$102$	1.37587	−	1.37587i	0.136232	−	0.136232i
$103$	1.15730	+	1.15730i	0.114032	+	0.114032i	0.761820	−	0.647788i	$-0.224306\pi$
$103$	1.15730	+	1.15730i	0.114032	+	0.114032i	−0.647788	+	0.761820i	$0.724306\pi$
$104$		−	4.81645i		−	0.472292i
$105$	−6.75371	+	5.22397i	−0.659094	+	0.509808i
$106$			8.99421i			0.873595i
$107$	5.83276	−	5.83276i	0.563874	−	0.563874i	−0.366531	−	0.930406i	$-0.619455\pi$
$107$	5.83276	−	5.83276i	0.563874	−	0.563874i	0.930406	+	0.366531i	$0.119455\pi$
$108$	12.1807	−	12.1807i	1.17209	−	1.17209i
$109$	5.99257			0.573984			0.286992	−	0.957933i	$-0.407345\pi$
$109$	5.99257			0.573984			0.286992	+	0.957933i	$0.407345\pi$
$110$	−4.61807	−	0.589797i	−0.440315	−	0.0562349i
$111$		−	7.92752i		−	0.752447i
$112$	−6.43206	+	6.43206i	−0.607772	+	0.607772i
$113$	4.04562	+	4.04562i	0.380580	+	0.380580i	0.871311	−	0.490731i	$-0.163270\pi$
$113$	4.04562	+	4.04562i	0.380580	+	0.380580i	−0.490731	+	0.871311i	$0.663270\pi$
$114$	15.1505			1.41897
$115$	−10.1268	+	3.52827i	−0.944325	+	0.329013i
$116$	12.0304			1.11699
$117$	1.86221	+	1.86221i	0.172161	+	0.172161i
$118$	−9.99395	+	9.99395i	−0.920018	+	0.920018i
$119$		−	3.81110i		−	0.349363i
$120$	−6.38405	+	4.93805i	−0.582782	+	0.450780i
$121$	10.2361			0.930557
$122$	−12.9033	+	12.9033i	−1.16821	+	1.16821i
$123$	5.34116	−	5.34116i	0.481596	−	0.481596i
$124$		−	1.22204i		−	0.109743i
$125$	−10.2789	+	4.39823i	−0.919372	+	0.393390i
$126$		−	21.9366i		−	1.95427i
$127$	−7.88018	−	7.88018i	−0.699253	−	0.699253i	0.264997	−	0.964249i	$-0.414629\pi$
$127$	−7.88018	−	7.88018i	−0.699253	−	0.699253i	−0.964249	+	0.264997i	$0.914629\pi$
$128$	14.6560	−	14.6560i	1.29542	−	1.29542i
$129$	7.11072			0.626064
$130$	−3.93419	−	5.08624i	−0.345052	−	0.446093i
$131$	−13.7748			−1.20351			−0.601756	−	0.798680i	$-0.705532\pi$
$131$	−13.7748			−1.20351			−0.601756	+	0.798680i	$0.705532\pi$
$132$	−2.05454	+	2.05454i	−0.178825	+	0.178825i
$133$	20.9830	−	20.9830i	1.81946	−	1.81946i
$134$	−23.8201			−2.05774
$135$	1.32787	−	10.3971i	0.114285	−	0.894842i
$136$		−	3.60250i		−	0.308912i
$137$	10.8487	−	10.8487i	0.926869	−	0.926869i	−0.0706334	−	0.997502i	$-0.522502\pi$
$137$	10.8487	−	10.8487i	0.926869	−	0.926869i	0.997502	+	0.0706334i	$0.0225020\pi$
$138$	−3.28162	+	9.80035i	−0.279350	+	0.834262i
$139$			6.60131i			0.559916i	0.960012	+	0.279958i	$0.0903205\pi$
$139$			6.60131i			0.559916i	−0.960012	+	0.279958i	$0.909680\pi$
$140$	−4.39409	+	34.4054i	−0.371368	+	2.90779i
$141$	−6.72389			−0.566253
$142$	−6.94878	−	6.94878i	−0.583129	−	0.583129i
$143$	−0.746031	−	0.746031i	−0.0623862	−	0.0623862i
$144$		−	4.70148i		−	0.391790i
$145$	5.79016	−	4.47867i	0.480846	−	0.371933i
$146$	21.0529			1.74235
$147$	6.91903	+	6.91903i	0.570672	+	0.570672i
$148$	−22.7715	−	22.7715i	−1.87180	−	1.87180i
$149$	5.41993			0.444018			0.222009	−	0.975045i	$-0.428739\pi$
$149$	5.41993			0.444018			0.222009	+	0.975045i	$0.428739\pi$
$150$	−2.70813	+	10.4293i	−0.221118	+	0.851549i
$151$	−11.2998			−0.919567			−0.459784	−	0.888031i	$-0.652073\pi$
$151$	−11.2998			−0.919567			−0.459784	+	0.888031i	$0.652073\pi$
$152$	19.8346	−	19.8346i	1.60880	−	1.60880i
$153$	1.39285	+	1.39285i	0.112605	+	0.112605i
$154$			8.78818i			0.708172i
$155$	−0.454944	−	0.588165i	−0.0365420	−	0.0472425i
$156$	−4.01312			−0.321307
$157$	−8.04085	+	8.04085i	−0.641729	+	0.641729i	−0.950980	−	0.309251i	$-0.899922\pi$
$157$	−8.04085	+	8.04085i	−0.641729	+	0.641729i	0.309251	+	0.950980i	$0.399922\pi$
$158$	25.1093	+	25.1093i	1.99759	+	1.99759i
$159$	3.41555			0.270870
$160$	0.806247	−	6.31285i	0.0637394	−	0.499075i
$161$	9.02827	+	18.1182i	0.711527	+	1.42791i
$162$	3.88166	+	3.88166i	0.304972	+	0.304972i
$163$	7.77915	−	7.77915i	0.609310	−	0.609310i	−0.333456	−	0.942766i	$-0.608215\pi$
$163$	7.77915	−	7.77915i	0.609310	−	0.609310i	0.942766	+	0.333456i	$0.108215\pi$
$164$		−	30.6845i		−	2.39606i
$165$	−0.223975	+	1.75371i	−0.0174364	+	0.136526i
$166$			15.0150i			1.16539i
$167$	−6.65328	−	6.65328i	−0.514846	−	0.514846i	0.401161	−	0.916007i	$-0.368607\pi$
$167$	−6.65328	−	6.65328i	−0.514846	−	0.514846i	−0.916007	+	0.401161i	$0.868607\pi$
$168$	10.7730	+	10.7730i	0.831154	+	0.831154i
$169$			11.5428i			0.887906i
$170$	−2.94261	−	3.80429i	−0.225688	−	0.291776i
$171$			15.3375i			1.17288i
$172$	20.4253	−	20.4253i	1.55741	−	1.55741i
$173$	−9.30402	+	9.30402i	−0.707372	+	0.707372i	−0.965982	−	0.258610i	$-0.916736\pi$
$173$	−9.30402	+	9.30402i	−0.707372	+	0.707372i	0.258610	+	0.965982i	$0.416736\pi$
$174$		−	7.05486i		−	0.534828i
$175$	10.6936	+	18.1950i	0.808361	+	1.37541i
$176$			1.88349i			0.141974i
$177$	3.79520	+	3.79520i	0.285264	+	0.285264i
$178$	−8.26802	−	8.26802i	−0.619715	−	0.619715i
$179$			14.0312i			1.04874i	0.851489	+	0.524372i	$0.175700\pi$
$179$			14.0312i			1.04874i	−0.851489	+	0.524372i	$0.824300\pi$
$180$	−10.9683	−	14.1802i	−0.817530	−	1.05693i
$181$		−	11.3603i		−	0.844402i	−0.906502	−	0.422201i	$-0.861258\pi$
$181$		−	11.3603i		−	0.844402i	0.906502	−	0.422201i	$-0.138742\pi$
$182$	−8.58294	+	8.58294i	−0.636210	+	0.636210i
$183$	4.90000	+	4.90000i	0.362219	+	0.362219i
$184$	8.53412	+	17.1265i	0.629144	+	1.26258i
$185$	−19.4372	−	2.48242i	−1.42905	−	0.182511i
$186$	−0.716633			−0.0525461
$187$	−0.558000	−	0.558000i	−0.0408050	−	0.0408050i
$188$	−19.3141	+	19.3141i	−1.40862	+	1.40862i
$189$	−19.7857			−1.43920
$190$	4.74423	−	37.1469i	0.344182	−	2.69492i
$191$		−	19.4523i		−	1.40752i	−0.710439	−	0.703759i	$-0.751504\pi$
$191$		−	19.4523i		−	1.40752i	0.710439	−	0.703759i	$-0.248496\pi$
$192$	−7.09409	−	7.09409i	−0.511972	−	0.511972i
$193$	−3.24826	+	3.24826i	−0.233815	+	0.233815i	−0.814283	−	0.580468i	$-0.802870\pi$
$193$	−3.24826	+	3.24826i	−0.233815	+	0.233815i	0.580468	+	0.814283i	$0.302870\pi$
$194$	27.6900			1.98803
$195$	−1.93150	+	1.49401i	−0.138317	+	0.106988i
$196$	39.7493			2.83923
$197$	8.33871	+	8.33871i	0.594109	+	0.594109i	0.938739	−	0.344630i	$-0.111996\pi$
$197$	8.33871	+	8.33871i	0.594109	+	0.594109i	−0.344630	+	0.938739i	$0.611996\pi$
$198$	−3.21184	−	3.21184i	−0.228256	−	0.228256i
$199$	6.09909			0.432353			0.216176	−	0.976354i	$-0.430641\pi$
$199$	6.09909			0.432353			0.216176	+	0.976354i	$0.430641\pi$
$200$	10.1083	+	17.1991i	0.714766	+	1.21616i
$201$			9.04567i			0.638032i
$202$	0.427818	+	0.427818i	0.0301011	+	0.0301011i
$203$	−9.77079	−	9.77079i	−0.685775	−	0.685775i
$204$	−3.00164			−0.210157
$205$	−11.4233	−	14.7683i	−0.797835	−	1.03146i
$206$		−	3.89888i		−	0.271648i
$207$	−9.92129	−	3.32212i	−0.689577	−	0.230903i
$208$	−1.83951	+	1.83951i	−0.127547	+	0.127547i
$209$		−	6.14444i		−	0.425020i
$210$	20.1761	+	2.57679i	1.39228	+	0.177815i
$211$	8.98215			0.618357			0.309178	−	0.951004i	$-0.399946\pi$
$211$	8.98215			0.618357			0.309178	+	0.951004i	$0.399946\pi$
$212$	9.81101	−	9.81101i	0.673823	−	0.673823i
$213$	−2.63879	+	2.63879i	−0.180807	+	0.180807i
$214$	−19.6502			−1.34326
$215$	2.22665	−	17.4345i	0.151856	−	1.18902i
$216$	−18.7028			−1.27256
$217$	−0.992518	+	0.992518i	−0.0673765	+	0.0673765i
$218$	−10.0943	−	10.0943i	−0.683673	−	0.683673i
$219$		−	7.99484i		−	0.540241i
$220$	4.39409	+	5.68081i	0.296250	+	0.383000i
$221$		−	1.08994i		−	0.0733171i
$222$	−13.3537	+	13.3537i	−0.896241	+	0.896241i
$223$	−1.83771	+	1.83771i	−0.123062	+	0.123062i	−0.765956	−	0.642893i	$-0.777734\pi$
$223$	−1.83771	+	1.83771i	−0.123062	+	0.123062i	0.642893	+	0.765956i	$0.277734\pi$
$224$	−12.0134			−0.802676
$225$	−10.5580	−	2.74155i	−0.703867	−	0.182770i
$226$		−	13.6295i		−	0.906618i
$227$	−4.53626	+	4.53626i	−0.301082	+	0.301082i	−0.841437	−	0.540355i	$-0.818290\pi$
$227$	−4.53626	+	4.53626i	−0.301082	+	0.301082i	0.540355	+	0.841437i	$0.318290\pi$
$228$	−16.5264	−	16.5264i	−1.09449	−	1.09449i
$229$	−17.3014			−1.14331			−0.571654	−	0.820495i	$-0.693698\pi$
$229$	−17.3014			−1.14331			−0.571654	+	0.820495i	$0.693698\pi$
$230$	23.0015	+	11.1150i	1.51668	+	0.732900i
$231$	3.33730			0.219578
$232$	−9.23600	−	9.23600i	−0.606373	−	0.606373i
$233$	−0.468284	+	0.468284i	−0.0306783	+	0.0306783i	−0.722280	−	0.691601i	$-0.756906\pi$
$233$	−0.468284	+	0.468284i	−0.0306783	+	0.0306783i	0.691601	+	0.722280i	$0.256906\pi$
$234$		−	6.27366i		−	0.410122i
$235$	−2.10552	+	16.4860i	−0.137349	+	1.07543i
$236$	21.8031			1.41926
$237$	9.53524	−	9.53524i	0.619381	−	0.619381i
$238$	−6.41968	+	6.41968i	−0.416126	+	0.416126i
$239$		−	7.68060i		−	0.496817i	−0.968655	−	0.248408i	$-0.920093\pi$
$239$		−	7.68060i		−	0.496817i	0.968655	−	0.248408i	$-0.0799075\pi$
$240$	4.32416	+	0.552260i	0.279123	+	0.0356483i
$241$			21.5909i			1.39079i	0.718626	+	0.695397i	$0.244771\pi$
$241$			21.5909i			1.39079i	−0.718626	+	0.695397i	$0.755229\pi$
$242$	−17.2425	−	17.2425i	−1.10839	−	1.10839i
$243$	11.4178	−	11.4178i	0.732449	−	0.732449i
$244$	28.1501			1.80213
$245$	19.1311	−	14.7979i	1.22224	−	0.945402i
$246$	−17.9941			−1.14726
$247$	6.00095	−	6.00095i	0.381831	−	0.381831i
$248$	−0.938194	+	0.938194i	−0.0595754	+	0.0595754i
$249$	5.70193			0.361345
$250$	24.7232	+	9.90580i	1.56363	+	0.626498i
$251$		−	4.66422i		−	0.294403i	−0.989107	−	0.147202i	$-0.952973\pi$
$251$		−	4.66422i		−	0.294403i	0.989107	−	0.147202i	$-0.0470266\pi$
$252$	−23.9288	+	23.9288i	−1.50737	+	1.50737i
$253$	3.97463	+	1.33090i	0.249883	+	0.0836727i
$254$			26.5479i			1.66576i
$255$	−1.44468	+	1.11745i	−0.0904692	+	0.0699777i
$256$	−27.1949			−1.69968
$257$	18.6888	+	18.6888i	1.16578	+	1.16578i	0.983189	+	0.182589i	$0.0584478\pi$
$257$	18.6888	+	18.6888i	1.16578	+	1.16578i	0.182589	+	0.983189i	$0.441552\pi$
$258$	−11.9778	−	11.9778i	−0.745706	−	0.745706i
$259$			36.9890i			2.29838i
$260$	−1.25667	+	9.83961i	−0.0779352	+	0.610227i
$261$	7.14192			0.442074
$262$	23.2033	+	23.2033i	1.43350	+	1.43350i
$263$	12.6761	+	12.6761i	0.781641	+	0.781641i	0.980108	−	0.198467i	$-0.0635962\pi$
$263$	12.6761	+	12.6761i	0.781641	+	0.781641i	−0.198467	+	0.980108i	$0.563596\pi$
$264$	3.15464			0.194155
$265$	1.06954	−	8.37445i	0.0657016	−	0.514438i
$266$	−70.6907			−4.33432
$267$	−3.13977	+	3.13977i	−0.192151	+	0.192151i
$268$	25.9833	+	25.9833i	1.58718	+	1.58718i
$269$		−	24.9626i		−	1.52200i	−0.648752	−	0.761000i	$-0.724709\pi$
$269$		−	24.9626i		−	1.52200i	0.648752	−	0.761000i	$-0.275291\pi$
$270$	−19.7504	+	15.2769i	−1.20197	+	0.929723i
$271$	−21.1040			−1.28198			−0.640990	−	0.767549i	$-0.721476\pi$
$271$	−21.1040			−1.28198			−0.640990	+	0.767549i	$0.721476\pi$
$272$	−1.37587	+	1.37587i	−0.0834246	+	0.0834246i
$273$	3.25937	+	3.25937i	0.197266	+	0.197266i
$274$	−36.5487			−2.20799
$275$	4.22971	+	1.09831i	0.255061	+	0.0662307i
$276$	14.2700	−	7.11072i	0.858953	−	0.428015i
$277$	−3.43111	−	3.43111i	−0.206155	−	0.206155i	0.596476	−	0.802631i	$-0.296567\pi$
$277$	−3.43111	−	3.43111i	−0.206155	−	0.206155i	−0.802631	+	0.596476i	$0.796567\pi$
$278$	11.1197	−	11.1197i	0.666916	−	0.666916i
$279$		−	0.725477i		−	0.0434331i
$280$	29.7873	−	23.0404i	1.78013	−	1.37693i
$281$		−	24.9325i		−	1.48735i	−0.668541	−	0.743675i	$-0.733081\pi$
$281$		−	24.9325i		−	1.48735i	0.668541	−	0.743675i	$-0.266919\pi$
$282$	11.3262	+	11.3262i	0.674465	+	0.674465i
$283$	14.1092	+	14.1092i	0.838702	+	0.838702i	0.988688	−	0.149986i	$-0.0479228\pi$
$283$	14.1092	+	14.1092i	0.838702	+	0.838702i	−0.149986	+	0.988688i	$0.547923\pi$
$284$			15.1597i			0.899560i
$285$	−14.1065	−	1.80162i	−0.835598	−	0.106719i
$286$			2.51334i			0.148617i
$287$	−24.9213	+	24.9213i	−1.47106	+	1.47106i
$288$	4.39055	−	4.39055i	0.258716	−	0.258716i
$289$			16.1848i			0.952045i
$290$	−17.2975	−	2.20916i	−1.01575	−	0.129726i
$291$		−	10.5153i		−	0.616416i
$292$	−22.9648	−	22.9648i	−1.34392	−	1.34392i
$293$	0.599295	+	0.599295i	0.0350112	+	0.0350112i	0.724396	−	0.689384i	$-0.242119\pi$
$293$	0.599295	+	0.599295i	0.0350112	+	0.0350112i	−0.689384	+	0.724396i	$0.742119\pi$
$294$		−	23.3098i		−	1.35946i
$295$	10.4937	−	8.11687i	0.610968	−	0.472582i
$296$			34.9645i			2.03227i
$297$	−2.89692	+	2.89692i	−0.168096	+	0.168096i
$298$	−9.12971	−	9.12971i	−0.528870	−	0.528870i
$299$	2.58200	+	5.18163i	0.149321	+	0.299661i
$300$	14.3305	−	8.42236i	0.827372	−	0.486265i
$301$	−33.1779			−1.91234
$302$	19.0343	+	19.0343i	1.09530	+	1.09530i
$303$	0.162463	−	0.162463i	0.00933328	−	0.00933328i
$304$	−15.1505			−0.868941
$305$	13.5485	−	10.4797i	0.775786	−	0.600069i
$306$		−	4.69244i		−	0.268249i
$307$	−6.58285	−	6.58285i	−0.375703	−	0.375703i	0.493846	−	0.869549i	$-0.335591\pi$
$307$	−6.58285	−	6.58285i	−0.375703	−	0.375703i	−0.869549	+	0.493846i	$0.835591\pi$
$308$	9.58627	−	9.58627i	0.546228	−	0.546228i
$309$	−1.48060			−0.0842282
$310$	−0.224407	+	1.75709i	−0.0127454	+	0.0997958i
$311$	8.24778			0.467689			0.233844	−	0.972274i	$-0.424869\pi$
$311$	8.24778			0.467689			0.233844	+	0.972274i	$0.424869\pi$
$312$	3.08097	+	3.08097i	0.174426	+	0.174426i
$313$	14.7382	+	14.7382i	0.833050	+	0.833050i	0.987933	−	0.154883i	$-0.0495000\pi$
$313$	14.7382	+	14.7382i	0.833050	+	0.833050i	−0.154883	+	0.987933i	$0.549500\pi$
$314$	27.0892			1.52873
$315$	−2.60859	+	20.4250i	−0.146977	+	1.15082i
$316$		−	54.7792i		−	3.08157i
$317$	19.7503	+	19.7503i	1.10929	+	1.10929i	0.993244	+	0.116044i	$0.0370215\pi$
$317$	19.7503	+	19.7503i	1.10929	+	1.10929i	0.116044	+	0.993244i	$0.462978\pi$
$318$	−5.75339	−	5.75339i	−0.322634	−	0.322634i
$319$	−2.86117			−0.160195
$320$	−19.6152	+	15.1723i	−1.09652	+	0.848156i
$321$			7.46216i			0.416497i
$322$	15.3117	−	45.7274i	0.853288	−	2.54829i
$323$	4.48846	−	4.48846i	0.249744	−	0.249744i
$324$		−	8.46834i		−	0.470464i
$325$	3.05827	+	5.20359i	0.169642	+	0.288643i
$326$	−26.2075			−1.45150
$327$	−3.83331	+	3.83331i	−0.211982	+	0.211982i
$328$	−23.5573	+	23.5573i	−1.30073	+	1.30073i
$329$	31.3730			1.72965
$330$	3.33135	−	2.57679i	0.183385	−	0.141848i
$331$	4.89170			0.268872			0.134436	−	0.990922i	$-0.457078\pi$
$331$	4.89170			0.268872			0.134436	+	0.990922i	$0.457078\pi$
$332$	16.3786	−	16.3786i	0.898891	−	0.898891i
$333$	−13.5185	−	13.5185i	−0.740807	−	0.740807i
$334$			22.4145i			1.22647i
$335$	22.1787	+	2.83256i	1.21175	+	0.154759i
$336$		−	8.22887i		−	0.448922i
$337$	23.4893	−	23.4893i	1.27954	−	1.27954i	0.338620	−	0.940923i	$-0.390040\pi$
$337$	23.4893	−	23.4893i	1.27954	−	1.27954i	0.940923	−	0.338620i	$-0.109960\pi$
$338$	19.4435	−	19.4435i	1.05759	−	1.05759i
$339$	−5.17577			−0.281109
$340$	−0.939935	+	7.35962i	−0.0509751	+	0.399131i
$341$			0.290638i			0.0157389i
$342$	25.8355	−	25.8355i	1.39702	−	1.39702i
$343$	−11.3908	−	11.3908i	−0.615046	−	0.615046i
$344$	−31.3620			−1.69092
$345$	4.22090	−	8.73481i	0.227246	−	0.470266i
$346$	31.3447			1.68510
$347$	−2.55011	−	2.55011i	−0.136897	−	0.136897i	0.635337	−	0.772235i	$-0.280861\pi$
$347$	−2.55011	−	2.55011i	−0.136897	−	0.136897i	−0.772235	+	0.635337i	$0.780861\pi$
$348$	−7.69554	+	7.69554i	−0.412524	+	0.412524i
$349$		−	0.0936127i		−	0.00501097i	−0.999997	−	0.00250549i	$-0.999202\pi$
$349$		−	0.0936127i		−	0.00501097i	0.999997	−	0.00250549i	$-0.000797522\pi$
$350$	12.6359	−	48.6620i	0.675415	−	2.60110i
$351$	−5.65853			−0.302030
$352$	−1.75893	+	1.75893i	−0.0937513	+	0.0937513i
$353$	−11.9728	+	11.9728i	−0.637250	+	0.637250i	−0.949876	−	0.312626i	$-0.898791\pi$
$353$	−11.9728	+	11.9728i	−0.637250	+	0.637250i	0.312626	+	0.949876i	$0.398791\pi$
$354$		−	12.7858i		−	0.679557i
$355$	5.64365	+	7.29627i	0.299534	+	0.387246i
$356$			18.0377i			0.955999i
$357$	2.43787	+	2.43787i	0.129026	+	0.129026i
$358$	23.6352	−	23.6352i	1.24916	−	1.24916i
$359$	−4.27854			−0.225812			−0.112906	−	0.993606i	$-0.536016\pi$
$359$	−4.27854			−0.225812			−0.112906	+	0.993606i	$0.536016\pi$
$360$	−2.46581	+	19.3071i	−0.129960	+	1.01757i
$361$	30.4249			1.60131
$362$	−19.1361	+	19.1361i	−1.00577	+	1.00577i
$363$	−6.54781	+	6.54781i	−0.343671	+	0.343671i
$364$	18.7248			0.981446
$365$	−19.6022	−	2.50350i	−1.02603	−	0.131039i
$366$		−	16.5078i		−	0.862878i
$367$	−2.09006	+	2.09006i	−0.109100	+	0.109100i	−0.759550	−	0.650449i	$-0.774581\pi$
$367$	−2.09006	+	2.09006i	−0.109100	+	0.109100i	0.650449	+	0.759550i	$0.274581\pi$
$368$	3.28162	−	9.80035i	0.171066	−	0.510879i
$369$		−	18.2161i		−	0.948293i
$370$	28.5598	+	36.9230i	1.48475	+	1.91953i
$371$	−15.9366			−0.827386
$372$	0.781714	+	0.781714i	0.0405300	+	0.0405300i
$373$	−7.37682	−	7.37682i	−0.381957	−	0.381957i	0.489850	−	0.871807i	$-0.337052\pi$
$373$	−7.37682	−	7.37682i	−0.381957	−	0.381957i	−0.871807	+	0.489850i	$0.837052\pi$
$374$			1.87987i			0.0972057i
$375$	3.76172	−	9.38861i	0.194254	−	0.484826i
$376$	29.6558			1.52938
$377$	−2.79435	−	2.79435i	−0.143916	−	0.143916i
$378$	33.3285	+	33.3285i	1.71423	+	1.71423i
$379$	−13.7503			−0.706308			−0.353154	−	0.935565i	$-0.614891\pi$
$379$	−13.7503			−0.706308			−0.353154	+	0.935565i	$0.614891\pi$
$380$	−45.6955	+	35.3453i	−2.34413	+	1.81318i
$381$	10.0815			0.516493
$382$	−32.7668	+	32.7668i	−1.67650	+	1.67650i
$383$	4.93055	+	4.93055i	0.251939	+	0.251939i	0.821765	−	0.569826i	$-0.192989\pi$
$383$	4.93055	+	4.93055i	0.251939	+	0.251939i	−0.569826	+	0.821765i	$0.692989\pi$
$384$			18.7501i			0.956839i
$385$	1.04504	−	8.18261i	0.0532603	−	0.417024i
$386$	10.9432			0.556995
$387$	12.1256	−	12.1256i	0.616380	−	0.616380i
$388$	−30.2047	−	30.2047i	−1.53341	−	1.53341i
$389$	1.98718			0.100754			0.0503769	−	0.998730i	$-0.483958\pi$
$389$	1.98718			0.100754			0.0503769	+	0.998730i	$0.483958\pi$
$390$	5.77016	+	0.736937i	0.292183	+	0.0373163i
$391$	1.93123	+	3.87564i	0.0976663	+	0.196000i
$392$	−30.5165	−	30.5165i	−1.54132	−	1.54132i
$393$	8.81143	−	8.81143i	0.444478	−	0.444478i
$394$		−	28.0926i		−	1.41529i
$395$	−20.3932	−	26.3650i	−1.02610	−	1.32657i
$396$			7.00704i			0.352117i
$397$	−17.8915	−	17.8915i	−0.897948	−	0.897948i	0.0973067	−	0.995254i	$-0.468977\pi$
$397$	−17.8915	−	17.8915i	−0.897948	−	0.897948i	−0.995254	+	0.0973067i	$0.968977\pi$
$398$	−10.2737	−	10.2737i	−0.514976	−	0.514976i
$399$			26.8447i			1.34392i
$400$	2.70813	−	10.4293i	0.135407	−	0.521465i
$401$		−	13.4025i		−	0.669289i	−0.942344	−	0.334645i	$-0.891384\pi$
$401$		−	13.4025i		−	0.669289i	0.942344	−	0.334645i	$-0.108616\pi$
$402$	15.2372	−	15.2372i	0.759961	−	0.759961i
$403$	−0.283851	+	0.283851i	−0.0141396	+	0.0141396i
$404$		−	0.933339i		−	0.0464353i
$405$	−3.15260	−	4.07578i	−0.156654	−	0.202527i
$406$			32.9172i			1.63366i
$407$	5.41572	+	5.41572i	0.268447	+	0.268447i
$408$	2.30444	+	2.30444i	0.114087	+	0.114087i
$409$		−	4.34330i		−	0.214762i	−0.994218	−	0.107381i	$-0.965753\pi$
$409$		−	4.34330i		−	0.214762i	0.994218	−	0.107381i	$-0.0342465\pi$
$410$	−5.63466	+	44.1190i	−0.278276	+	2.17888i
$411$			13.8794i			0.684618i
$412$	−4.25295	+	4.25295i	−0.209528	+	0.209528i
$413$	−17.7080	−	17.7080i	−0.871353	−	0.871353i
$414$	11.1161	+	22.3081i	0.546327	+	1.09639i
$415$	1.78550	−	13.9804i	0.0876469	−	0.686269i
$416$	−3.43570			−0.168449
$417$	−4.22270	−	4.22270i	−0.206787	−	0.206787i
$418$	−10.3501	+	10.3501i	−0.506242	+	0.506242i
$419$	−17.8529			−0.872173			−0.436086	−	0.899905i	$-0.643636\pi$
$419$	−17.8529			−0.872173			−0.436086	+	0.899905i	$0.643636\pi$
$420$	−19.1975	−	24.8191i	−0.936744	−	1.21105i
$421$		−	4.91938i		−	0.239756i	−0.992789	−	0.119878i	$-0.961750\pi$
$421$		−	4.91938i		−	0.239756i	0.992789	−	0.119878i	$-0.0382504\pi$
$422$	−15.1302	−	15.1302i	−0.736526	−	0.736526i
$423$	−11.4660	+	11.4660i	−0.557494	+	0.557494i
$424$	−15.0643			−0.731588
$425$	2.28746	+	3.89207i	0.110958	+	0.188793i
$426$	8.88995			0.430719
$427$	−22.8629	−	22.8629i	−1.10641	−	1.10641i
$428$	21.4348	+	21.4348i	1.03609	+	1.03609i
$429$	0.954437			0.0460806
$430$	−33.1187	+	25.6172i	−1.59712	+	1.23537i
$431$			12.3698i			0.595831i	0.954592	+	0.297915i	$0.0962913\pi$
$431$			12.3698i			0.595831i	−0.954592	+	0.297915i	$0.903709\pi$
$432$	7.14300	+	7.14300i	0.343668	+	0.343668i
$433$	6.77752	+	6.77752i	0.325707	+	0.325707i	0.850951	−	0.525244i	$-0.176026\pi$
$433$	6.77752	+	6.77752i	0.325707	+	0.325707i	−0.525244	+	0.850951i	$0.676026\pi$
$434$	3.34374			0.160505
$435$	−0.838926	+	6.56873i	−0.0402234	+	0.314946i
$436$			22.0220i			1.05466i
$437$	−10.7055	+	31.9713i	−0.512114	+	1.52939i
$438$	−13.4671	+	13.4671i	−0.643482	+	0.643482i
$439$			17.7444i			0.846896i	0.905921	+	0.423448i	$0.139180\pi$
$439$			17.7444i			0.846896i	−0.905921	+	0.423448i	$0.860820\pi$
$440$	0.987845	−	7.73475i	0.0470936	−	0.368740i
$441$	23.5975			1.12369
$442$	−1.83597	+	1.83597i	−0.0873281	+	0.0873281i
$443$	5.54990	−	5.54990i	0.263684	−	0.263684i	−0.562865	−	0.826549i	$-0.690301\pi$
$443$	5.54990	−	5.54990i	0.263684	−	0.263684i	0.826549	+	0.562865i	$0.190301\pi$
$444$	29.1328			1.38258
$445$	6.71511	+	8.68149i	0.318327	+	0.411542i
$446$	6.19115			0.293159
$447$	−3.46700	+	3.46700i	−0.163984	+	0.163984i
$448$	33.1003	+	33.1003i	1.56384	+	1.56384i
$449$			18.5203i			0.874028i	0.899455	+	0.437014i	$0.143964\pi$
$449$			18.5203i			0.874028i	−0.899455	+	0.437014i	$0.856036\pi$
$450$	13.1666	+	22.4027i	0.620679	+	1.05607i
$451$			7.29768i			0.343634i
$452$	−14.8672	+	14.8672i	−0.699294	+	0.699294i
$453$	7.22824	−	7.22824i	0.339612	−	0.339612i
$454$	15.2824			0.717238
$455$	9.01216	−	6.97088i	0.422496	−	0.326800i
$456$			25.3754i			1.18831i
$457$	−6.04117	+	6.04117i	−0.282594	+	0.282594i	−0.834143	−	0.551549i	$-0.814037\pi$
$457$	−6.04117	+	6.04117i	−0.282594	+	0.282594i	0.551549	+	0.834143i	$0.314037\pi$
$458$	29.1437	+	29.1437i	1.36180	+	1.36180i
$459$	−4.23234			−0.197549
$460$	−12.9660	−	37.2147i	−0.604543	−	1.73515i
$461$	33.3169			1.55172			0.775861	−	0.630904i	$-0.217316\pi$
$461$	33.3169			1.55172			0.775861	+	0.630904i	$0.217316\pi$
$462$	−5.62159	−	5.62159i	−0.261540	−	0.261540i
$463$	5.46719	−	5.46719i	0.254082	−	0.254082i	−0.568560	−	0.822642i	$-0.692499\pi$
$463$	5.46719	−	5.46719i	0.254082	−	0.254082i	0.822642	+	0.568560i	$0.192499\pi$
$464$			7.05486i			0.327514i
$465$	0.667252	+	0.0852182i	0.0309431	+	0.00395190i
$466$	1.57762			0.0730819
$467$	12.9751	−	12.9751i	0.600416	−	0.600416i	−0.340007	−	0.940423i	$-0.610429\pi$
$467$	12.9751	−	12.9751i	0.600416	−	0.600416i	0.940423	+	0.340007i	$0.110429\pi$
$468$	−6.84340	+	6.84340i	−0.316336	+	0.316336i
$469$		−	42.2062i		−	1.94890i
$470$	31.3170	−	24.2236i	1.44454	−	1.11735i
$471$		−	10.2871i		−	0.474004i
$472$	−16.7388	−	16.7388i	−0.770464	−	0.770464i
$473$	−4.85772	+	4.85772i	−0.223358	+	0.223358i
$474$	−32.1237			−1.47549
$475$	−8.83463	+	34.0231i	−0.405361	+	1.56109i
$476$	14.0054			0.641934
$477$	5.82439	−	5.82439i	0.266680	−	0.266680i
$478$	−12.9378	+	12.9378i	−0.591759	+	0.591759i
$479$	−18.4856			−0.844629			−0.422314	−	0.906449i	$-0.638782\pi$
$479$	−18.4856			−0.844629			−0.422314	+	0.906449i	$0.638782\pi$
$480$	3.52245	+	4.55392i	0.160777	+	0.207857i
$481$			10.5785i			0.482338i
$482$	36.3693	−	36.3693i	1.65658	−	1.65658i
$483$	−17.3650	−	5.81461i	−0.790133	−	0.264574i
$484$			37.6166i			1.70985i
$485$	−25.7820	−	3.29275i	−1.17070	−	0.149516i
$486$	−38.4658			−1.74484
$487$	−5.37721	−	5.37721i	−0.243664	−	0.243664i	0.574700	−	0.818364i	$-0.305119\pi$
$487$	−5.37721	−	5.37721i	−0.243664	−	0.243664i	−0.818364	+	0.574700i	$0.805119\pi$
$488$	−21.6115	−	21.6115i	−0.978308	−	0.978308i
$489$			9.95228i			0.450058i
$490$	−57.1525	−	7.29924i	−2.58189	−	0.329746i
$491$	−6.57507			−0.296729			−0.148364	−	0.988933i	$-0.547401\pi$
$491$	−6.57507			−0.296729			−0.148364	+	0.988933i	$0.547401\pi$
$492$	19.6282	+	19.6282i	0.884906	+	0.884906i
$493$	−2.09006	−	2.09006i	−0.0941315	−	0.0941315i
$494$	−20.2168			−0.909599
$495$	2.60859	+	3.37246i	0.117247	+	0.151581i
$496$	0.716633			0.0321778
$497$	12.3123	−	12.3123i	0.552284	−	0.552284i
$498$	−9.60475	−	9.60475i	−0.430399	−	0.430399i
$499$		−	16.2165i		−	0.725948i	−0.931799	−	0.362974i	$-0.881761\pi$
$499$		−	16.2165i		−	0.725948i	0.931799	−	0.362974i	$-0.118239\pi$
$500$	−16.1630	−	37.7738i	−0.722832	−	1.68929i
$501$	8.51189			0.380283
$502$	−7.85675	+	7.85675i	−0.350664	+	0.350664i
$503$	−29.7417	−	29.7417i	−1.32612	−	1.32612i	−0.908728	−	0.417389i	$-0.862945\pi$
$503$	−29.7417	−	29.7417i	−1.32612	−	1.32612i	−0.417389	−	0.908728i	$-0.637055\pi$
$504$	36.7414			1.63659
$505$	−0.347464	−	0.449212i	−0.0154619	−	0.0199897i
$506$	−4.45330	−	8.93702i	−0.197973	−	0.397299i
$507$	−7.38365	−	7.38365i	−0.327919	−	0.327919i
$508$	28.9588	−	28.9588i	1.28484	−	1.28484i
$509$			4.84148i			0.214595i	0.994227	+	0.107297i	$0.0342197\pi$
$509$			4.84148i			0.214595i	−0.994227	+	0.107297i	$0.965780\pi$
$510$	4.31584	+	0.551198i	0.191109	+	0.0244075i
$511$			37.3031i			1.65019i
$512$	16.4971	+	16.4971i	0.729074	+	0.729074i
$513$	−23.3023	−	23.3023i	−1.02882	−	1.02882i
$514$		−	62.9617i		−	2.77712i
$515$	−0.463634	+	3.63022i	−0.0204302	+	0.159967i
$516$			26.1311i			1.15036i
$517$	4.59346	−	4.59346i	0.202020	−	0.202020i
$518$	62.3069	−	62.3069i	2.73761	−	2.73761i
$519$		−	11.9031i		−	0.522490i
$520$	8.51889	−	6.58934i	0.373578	−	0.288962i
$521$		−	9.28769i		−	0.406901i	−0.979085	−	0.203450i	$-0.934784\pi$
$521$		−	9.28769i		−	0.406901i	0.979085	−	0.203450i	$-0.0652156\pi$
$522$	−12.0304	−	12.0304i	−0.526554	−	0.526554i
$523$	−1.62080	−	1.62080i	−0.0708725	−	0.0708725i	0.670782	−	0.741655i	$-0.265959\pi$
$523$	−1.62080	−	1.62080i	−0.0708725	−	0.0708725i	−0.741655	+	0.670782i	$0.765959\pi$
$524$		−	50.6209i		−	2.21139i
$525$	−18.4794	−	4.79846i	−0.806506	−	0.209422i
$526$		−	42.7050i		−	1.86203i
$527$	−0.212308	+	0.212308i	−0.00924830	+	0.00924830i
$528$	−1.20483	−	1.20483i	−0.0524333	−	0.0524333i
$529$	−18.3623	−	13.8501i	−0.798363	−	0.602177i
$530$	−15.9081	+	12.3049i	−0.691005	+	0.534491i
$531$	12.9436			0.561703
$532$	77.1103	+	77.1103i	3.34316	+	3.34316i
$533$	−7.12725	+	7.12725i	−0.308715	+	0.308715i
$534$	10.5777			0.457743
$535$	18.2962	+	2.33670i	0.791014	+	0.101024i
$536$		−	39.8961i		−	1.72325i
$537$	−8.97546	−	8.97546i	−0.387320	−	0.387320i
$538$	−42.0489	+	42.0489i	−1.81286	+	1.81286i
$539$	−9.45354			−0.407193
$540$	38.2083	+	4.87978i	1.64422	+	0.209992i
$541$	7.32758			0.315037			0.157519	−	0.987516i	$-0.449651\pi$
$541$	7.32758			0.315037			0.157519	+	0.987516i	$0.449651\pi$
$542$	35.5492	+	35.5492i	1.52697	+	1.52697i
$543$	7.26690	+	7.26690i	0.311853	+	0.311853i
$544$	−2.56976			−0.110178
$545$	8.19838	+	10.5991i	0.351180	+	0.454016i
$546$		−	10.9806i		−	0.469927i
$547$	−14.1883	−	14.1883i	−0.606648	−	0.606648i	0.335421	−	0.942068i	$-0.391122\pi$
$547$	−14.1883	−	14.1883i	−0.606648	−	0.606648i	−0.942068	+	0.335421i	$0.891122\pi$
$548$	39.8679	+	39.8679i	1.70307	+	1.70307i
$549$	16.7115			0.713231
$550$	−5.27475	−	8.97490i	−0.224916	−	0.382691i
$551$		−	23.0148i		−	0.980463i
$552$	−16.4145	−	5.49636i	−0.698648	−	0.233940i
$553$	−44.4904	+	44.4904i	−1.89193	+	1.89193i
$554$			11.5592i			0.491104i
$555$	14.0215	−	10.8456i	0.595178	−	0.460369i
$556$	−24.2591			−1.02881
$557$	11.1665	−	11.1665i	0.473140	−	0.473140i	−0.429789	−	0.902929i	$-0.641412\pi$
$557$	11.1665	−	11.1665i	0.473140	−	0.473140i	0.902929	+	0.429789i	$0.141412\pi$
$558$	−1.22204	+	1.22204i	−0.0517333	+	0.0517333i
$559$	−9.48856			−0.401323
$560$	−20.1761	−	2.57679i	−0.852594	−	0.108889i
$561$	0.713879			0.0301400
$562$	−41.9981	+	41.9981i	−1.77158	+	1.77158i
$563$	6.69838	+	6.69838i	0.282303	+	0.282303i	0.834027	−	0.551724i	$-0.186030\pi$
$563$	6.69838	+	6.69838i	0.282303	+	0.282303i	−0.551724	+	0.834027i	$0.686030\pi$
$564$		−	24.7095i		−	1.04046i
$565$	−1.62074	+	12.6903i	−0.0681851	+	0.533884i
$566$		−	47.5330i		−	1.99796i
$567$	−6.87780	+	6.87780i	−0.288841	+	0.288841i
$568$	11.6384	−	11.6384i	0.488338	−	0.488338i
$569$	32.9802			1.38260			0.691301	−	0.722567i	$-0.257038\pi$
$569$	32.9802			1.38260			0.691301	+	0.722567i	$0.257038\pi$
$570$	20.7273	+	26.7968i	0.868169	+	1.12239i
$571$			25.0848i			1.04977i	0.851175	+	0.524883i	$0.175891\pi$
$571$			25.0848i			1.04977i	−0.851175	+	0.524883i	$0.824109\pi$
$572$	2.74158	−	2.74158i	0.114631	−	0.114631i
$573$	12.4432	+	12.4432i	0.519821	+	0.519821i
$574$	83.9584			3.50436
$575$	−20.0948	−	13.0843i	−0.838012	−	0.545652i
$576$	−24.1945			−1.00810
$577$	26.2016	+	26.2016i	1.09079	+	1.09079i	0.995444	+	0.0953431i	$0.0303948\pi$
$577$	26.2016	+	26.2016i	1.09079	+	1.09079i	0.0953431	+	0.995444i	$0.469605\pi$
$578$	27.2628	−	27.2628i	1.13398	−	1.13398i
$579$		−	4.15568i		−	0.172704i
$580$	16.4586	+	21.2782i	0.683407	+	0.883529i
$581$	−26.6046			−1.10375
$582$	−17.7127	+	17.7127i	−0.734213	+	0.734213i
$583$	−2.33335	+	2.33335i	−0.0966373	+	0.0966373i
$584$			35.2613i			1.45912i
$585$	−0.746031	+	5.84136i	−0.0308446	+	0.241511i
$586$		−	2.01899i		−	0.0834038i
$587$	−6.28335	−	6.28335i	−0.259342	−	0.259342i	0.565445	−	0.824786i	$-0.308705\pi$
$587$	−6.28335	−	6.28335i	−0.259342	−	0.259342i	−0.824786	+	0.565445i	$0.808705\pi$
$588$	−25.4267	+	25.4267i	−1.04858	+	1.04858i
$589$	−2.33784			−0.0963292
$590$	−31.3490	−	4.00374i	−1.29062	−	0.164832i
$591$	−10.6682			−0.438829
$592$	13.3537	−	13.3537i	0.548833	−	0.548833i
$593$	−16.2783	+	16.2783i	−0.668469	+	0.668469i	−0.957362	−	0.288892i	$-0.906713\pi$
$593$	−16.2783	+	16.2783i	−0.668469	+	0.668469i	0.288892	+	0.957362i	$0.406713\pi$
$594$	9.75956			0.400439
$595$	6.74071	−	5.21392i	0.276342	−	0.213750i
$596$			19.9176i			0.815858i
$597$	−3.90144	+	3.90144i	−0.159675	+	0.159675i
$598$	4.37900	−	13.0776i	0.179071	−	0.534783i
$599$		−	17.3527i		−	0.709011i	−0.935054	−	0.354505i	$-0.884649\pi$
$599$		−	17.3527i		−	0.709011i	0.935054	−	0.354505i	$-0.115351\pi$
$600$	−17.4679	−	4.53582i	−0.713125	−	0.185174i
$601$	1.29500			0.0528243			0.0264122	−	0.999651i	$-0.491592\pi$
$601$	1.29500			0.0528243			0.0264122	+	0.999651i	$0.491592\pi$
$602$	55.8872	+	55.8872i	2.27779	+	2.27779i
$603$	15.4252	+	15.4252i	0.628163	+	0.628163i
$604$		−	41.5256i		−	1.68965i
$605$	14.0040	+	18.1047i	0.569342	+	0.736062i
$606$	−0.547330			−0.0222338
$607$	15.7734	+	15.7734i	0.640223	+	0.640223i	0.950610	−	0.310387i	$-0.100459\pi$
$607$	15.7734	+	15.7734i	0.640223	+	0.640223i	−0.310387	+	0.950610i	$0.600459\pi$
$608$	−14.1485	−	14.1485i	−0.573799	−	0.573799i
$609$	12.5003			0.506538
$610$	−40.4749	−	5.16926i	−1.63878	−	0.209297i
$611$	8.97237			0.362983
$612$	−5.11858	+	5.11858i	−0.206906	+	0.206906i
$613$	−20.2850	−	20.2850i	−0.819303	−	0.819303i	0.166704	−	0.986007i	$-0.446688\pi$
$613$	−20.2850	−	20.2850i	−0.819303	−	0.819303i	−0.986007	+	0.166704i	$0.946688\pi$
$614$			22.1773i			0.895001i
$615$	16.7541	+	2.13976i	0.675592	+	0.0862834i
$616$	−14.7192			−0.593055
$617$	−17.0272	+	17.0272i	−0.685488	+	0.685488i	−0.961231	−	0.275743i	$-0.911076\pi$
$617$	−17.0272	+	17.0272i	−0.685488	+	0.685488i	0.275743	+	0.961231i	$0.411076\pi$
$618$	2.49402	+	2.49402i	0.100324	+	0.100324i
$619$	43.8905			1.76411			0.882053	−	0.471150i	$-0.156161\pi$
$619$	43.8905			1.76411			0.882053	+	0.471150i	$0.156161\pi$
$620$	2.16144	−	1.67187i	0.0868055	−	0.0671439i
$621$	20.1208	−	10.0262i	0.807421	−	0.402337i
$622$	−13.8932	−	13.8932i	−0.557065	−	0.557065i
$623$	14.6499	−	14.6499i	0.586934	−	0.586934i
$624$		−	2.35338i		−	0.0942105i
$625$	−21.8416	−	12.1632i	−0.873666	−	0.486527i
$626$		−	49.6520i		−	1.98449i
$627$	3.93046	+	3.93046i	0.156967	+	0.156967i
$628$	−29.5492	−	29.5492i	−1.17914	−	1.17914i
$629$			7.91227i			0.315483i
$630$	38.7995	−	30.0113i	1.54581	−	1.19568i
$631$			12.7505i			0.507589i	0.967258	+	0.253794i	$0.0816787\pi$
$631$			12.7505i			0.507589i	−0.967258	+	0.253794i	$0.918321\pi$
$632$	−42.0553	+	42.0553i	−1.67287	+	1.67287i
$633$	−5.74567	+	5.74567i	−0.228370	+	0.228370i
$634$		−	66.5377i		−	2.64255i
$635$	3.15693	−	24.7185i	0.125279	−	0.980925i
$636$			12.5518i			0.497709i
$637$	−9.23276	−	9.23276i	−0.365815	−	0.365815i
$638$	4.81956	+	4.81956i	0.190808	+	0.190808i
$639$			8.99965i			0.356021i
$640$	45.9728	+	5.87142i	1.81723	+	0.232088i
$641$			34.9216i			1.37932i	0.724133	+	0.689661i	$0.242240\pi$
$641$			34.9216i			1.37932i	−0.724133	+	0.689661i	$0.757760\pi$
$642$	12.5698	−	12.5698i	0.496090	−	0.496090i
$643$	21.8497	+	21.8497i	0.861669	+	0.861669i	0.991532	−	0.129863i	$-0.0414537\pi$
$643$	21.8497	+	21.8497i	0.861669	+	0.861669i	−0.129863	+	0.991532i	$0.541454\pi$
$644$	−66.5823	+	33.1779i	−2.62371	+	1.30739i
$645$	9.72811	+	12.5768i	0.383044	+	0.495211i
$646$	−15.1214			−0.594942
$647$	−11.1217	−	11.1217i	−0.437238	−	0.437238i	0.453844	−	0.891081i	$-0.350052\pi$
$647$	−11.1217	−	11.1217i	−0.437238	−	0.437238i	−0.891081	+	0.453844i	$0.850052\pi$
$648$	−6.50136	+	6.50136i	−0.255397	+	0.255397i
$649$	−5.18541			−0.203545
$650$	3.61374	−	13.9169i	0.141742	−	0.545865i
$651$		−	1.26978i		−	0.0497667i
$652$	28.5875	+	28.5875i	1.11957	+	1.11957i
$653$	3.60860	−	3.60860i	0.141216	−	0.141216i	−0.632965	−	0.774180i	$-0.718162\pi$
$653$	3.60860	−	3.60860i	0.141216	−	0.141216i	0.774180	+	0.632965i	$0.218162\pi$
$654$	12.9142			0.504985
$655$	−18.8452	−	24.3636i	−0.736343	−	0.951965i
$656$	17.9941			0.702550
$657$	−13.6333	−	13.6333i	−0.531884	−	0.531884i
$658$	−52.8469	−	52.8469i	−2.06019	−	2.06019i
$659$	7.62542			0.297044			0.148522	−	0.988909i	$-0.452548\pi$
$659$	7.62542			0.297044			0.148522	+	0.988909i	$0.452548\pi$
$660$	−6.44468	−	0.823083i	−0.250859	−	0.0320385i
$661$		−	40.2447i		−	1.56534i	−0.622439	−	0.782668i	$-0.713858\pi$
$661$		−	40.2447i		−	1.56534i	0.622439	−	0.782668i	$-0.286142\pi$
$662$	−8.23994	−	8.23994i	−0.320254	−	0.320254i
$663$	0.697207	+	0.697207i	0.0270773	+	0.0270773i
$664$	−25.1485			−0.975950
$665$	65.8196	+	8.40616i	2.55237	+	0.325977i
$666$			45.5429i			1.76475i
$667$	14.8875	+	4.98504i	0.576446	+	0.193022i
$668$	24.4501	−	24.4501i	0.946001	−	0.946001i
$669$		−	2.35108i		−	0.0908981i
$670$	−32.5881	−	42.1308i	−1.25899	−	1.62766i
$671$	−6.69492			−0.258455
$672$	7.68466	−	7.68466i	0.296442	−	0.296442i
$673$	4.08508	−	4.08508i	0.157468	−	0.157468i	−0.623976	−	0.781444i	$-0.714484\pi$
$673$	4.08508	−	4.08508i	0.157468	−	0.157468i	0.781444	+	0.623976i	$0.214484\pi$
$674$	−79.1341			−3.04813
$675$	20.2061	−	11.8756i	0.777734	−	0.457092i
$676$	−42.4185			−1.63148
$677$	1.96550	−	1.96550i	0.0755401	−	0.0755401i	−0.668327	−	0.743867i	$-0.732989\pi$
$677$	1.96550	−	1.96550i	0.0755401	−	0.0755401i	0.743867	+	0.668327i	$0.232989\pi$
$678$	8.71844	+	8.71844i	0.334830	+	0.334830i
$679$			49.0631i			1.88287i
$680$	6.37177	−	4.92855i	0.244346	−	0.189001i
$681$		−	5.80348i		−	0.222390i
$682$	0.489572	−	0.489572i	0.0187467	−	0.0187467i
$683$	−26.6742	+	26.6742i	−1.02066	+	1.02066i	−0.0208762	+	0.999782i	$0.506646\pi$
$683$	−26.6742	+	26.6742i	−1.02066	+	1.02066i	−0.999782	+	0.0208762i	$0.993354\pi$
$684$	−56.3635			−2.15511
$685$	34.0303	+	4.34618i	1.30023	+	0.166059i
$686$			38.3750i			1.46517i
$687$	11.0673	−	11.0673i	0.422244	−	0.422244i
$688$	11.9778	+	11.9778i	0.456650	+	0.456650i
$689$	−4.55771			−0.173635
$690$	−21.8235	+	7.60355i	−0.830807	+	0.289462i
$691$	42.9820			1.63511			0.817556	−	0.575849i	$-0.195329\pi$
$691$	42.9820			1.63511			0.817556	+	0.575849i	$0.195329\pi$
$692$	−34.1913	−	34.1913i	−1.29976	−	1.29976i
$693$	5.69096	−	5.69096i	0.216182	−	0.216182i
$694$			8.59118i			0.326117i
$695$	−11.6758	+	9.03119i	−0.442888	+	0.342573i
$696$	11.8161			0.447889
$697$	−5.33088	+	5.33088i	−0.201922	+	0.201922i
$698$	−0.157688	+	0.157688i	−0.00596857	+	0.00596857i
$699$		−	0.599101i		−	0.0226601i
$700$	−66.8646	+	39.2978i	−2.52724	+	1.48532i
$701$			40.5427i			1.53128i	0.643272	+	0.765638i	$0.277576\pi$
$701$			40.5427i			1.53128i	−0.643272	+	0.765638i	$0.722424\pi$
$702$	9.53164	+	9.53164i	0.359748	+	0.359748i
$703$	−43.5632	+	43.5632i	−1.64302	+	1.64302i
$704$	9.69272			0.365308
$705$	−9.19889	−	11.8926i	−0.346450	−	0.447901i
$706$	40.3359			1.51806
$707$	−0.758037	+	0.758037i	−0.0285089	+	0.0285089i
$708$	−13.9469	+	13.9469i	−0.524157	+	0.524157i
$709$	39.8396			1.49621			0.748105	−	0.663581i	$-0.230964\pi$
$709$	39.8396			1.49621			0.748105	+	0.663581i	$0.230964\pi$
$710$	2.78380	−	21.7969i	0.104474	−	0.818024i
$711$		−	32.5201i		−	1.21960i
$712$	13.8480	−	13.8480i	0.518977	−	0.518977i
$713$	0.506381	−	1.51227i	0.0189641	−	0.0566351i
$714$		−	8.21304i		−	0.307365i
$715$	0.298872	−	2.34015i	0.0111772	−	0.0875166i
$716$	−51.5633			−1.92701
$717$	4.91310	+	4.91310i	0.183483	+	0.183483i
$718$	7.20707	+	7.20707i	0.268966	+	0.268966i
$719$		−	2.44123i		−	0.0910425i	−0.998963	−	0.0455213i	$-0.985505\pi$
$719$		−	2.44123i		−	0.0910425i	0.998963	−	0.0455213i	$-0.0144949\pi$
$720$	8.31555	−	6.43206i	0.309902	−	0.239709i
$721$	6.90831			0.257279
$722$	−51.2498	−	51.2498i	−1.90732	−	1.90732i
$723$	−13.8112	−	13.8112i	−0.513645	−	0.513645i
$724$	41.7477			1.55154
$725$	15.8429	+	4.11386i	0.588391	+	0.152785i
$726$	22.0592			0.818694
$727$	33.7202	−	33.7202i	1.25061	−	1.25061i	0.295166	−	0.955446i	$-0.404625\pi$
$727$	33.7202	−	33.7202i	1.25061	−	1.25061i	0.955446	−	0.295166i	$-0.0953750\pi$
$728$	−14.3755	−	14.3755i	−0.532791	−	0.532791i
$729$			7.69420i			0.284971i
$730$	28.8023	+	37.2365i	1.06602	+	1.37818i
$731$	−7.09704			−0.262494
$732$	−18.0070	+	18.0070i	−0.665557	+	0.665557i
$733$	19.6364	+	19.6364i	0.725286	+	0.725286i	0.969677	−	0.244391i	$-0.0785880\pi$
$733$	19.6364	+	19.6364i	0.725286	+	0.725286i	−0.244391	+	0.969677i	$0.578588\pi$
$734$	7.04129			0.259899
$735$	−2.77188	+	21.7036i	−0.102242	+	0.800550i
$736$	12.2168	−	6.08762i	0.450318	−	0.224393i
$737$	−6.17959	−	6.17959i	−0.227628	−	0.227628i
$738$	−30.6845	+	30.6845i	−1.12951	+	1.12951i
$739$			29.8720i			1.09886i	0.835540	+	0.549430i	$0.185155\pi$
$739$			29.8720i			1.09886i	−0.835540	+	0.549430i	$0.814845\pi$
$740$	9.12263	−	71.4295i	0.335355	−	2.62580i
$741$			7.67733i			0.282034i
$742$	26.8447	+	26.8447i	0.985501	+	0.985501i
$743$	17.4492	+	17.4492i	0.640149	+	0.640149i	0.950592	−	0.310443i	$-0.100477\pi$
$743$	17.4492	+	17.4492i	0.640149	+	0.640149i	−0.310443	+	0.950592i	$0.600477\pi$
$744$		−	1.20028i		−	0.0440045i
$745$	7.41495	+	9.58627i	0.271663	+	0.351214i
$746$			24.8521i			0.909900i
$747$	9.72327	−	9.72327i	0.355756	−	0.355756i
$748$	2.05059	−	2.05059i	0.0749769	−	0.0749769i
$749$		−	34.8177i		−	1.27221i
$750$	−22.1514	+	9.47834i	−0.808853	+	0.346100i
$751$			7.85854i			0.286762i	0.989668	+	0.143381i	$0.0457975\pi$
$751$			7.85854i			0.286762i	−0.989668	+	0.143381i	$0.954203\pi$
$752$	−11.3262	−	11.3262i	−0.413024	−	0.413024i
$753$	2.98360	+	2.98360i	0.108728	+	0.108728i
$754$			9.41402i			0.342838i
$755$	−15.4592	−	19.9861i	−0.562618	−	0.727369i
$756$		−	72.7104i		−	2.64445i
$757$	2.96142	−	2.96142i	0.107635	−	0.107635i	−0.651238	−	0.758873i	$-0.725750\pi$
$757$	2.96142	−	2.96142i	0.107635	−	0.107635i	0.758873	+	0.651238i	$0.225750\pi$
$758$	23.1621	+	23.1621i	0.841284	+	0.841284i
$759$	−3.39382	+	1.69114i	−0.123188	+	0.0613844i
$760$	62.2170	+	7.94606i	2.25685	+	0.288234i
$761$	23.6228			0.856327			0.428163	−	0.903701i	$-0.359161\pi$
$761$	23.6228			0.856327			0.428163	+	0.903701i	$0.359161\pi$
$762$	−16.9821	−	16.9821i	−0.615195	−	0.615195i
$763$	17.8858	−	17.8858i	0.647510	−	0.647510i
$764$	71.4850			2.58624
$765$	−0.558000	+	4.36909i	−0.0201745	+	0.157965i
$766$		−	16.6107i		−	0.600171i
$767$	−5.06431	−	5.06431i	−0.182862	−	0.182862i
$768$	17.3959	−	17.3959i	0.627721	−	0.627721i
$769$	−2.80397			−0.101114			−0.0505569	−	0.998721i	$-0.516100\pi$
$769$	−2.80397			−0.101114			−0.0505569	+	0.998721i	$0.516100\pi$
$770$	−15.5437	+	12.0230i	−0.560157	+	0.433280i
$771$	−23.9096			−0.861085
$772$	−11.9370	−	11.9370i	−0.429622	−	0.429622i
$773$	−8.92864	−	8.92864i	−0.321141	−	0.321141i	0.528064	−	0.849205i	$-0.322918\pi$
$773$	−8.92864	−	8.92864i	−0.321141	−	0.321141i	−0.849205	+	0.528064i	$0.822918\pi$
$774$	−40.8505			−1.46834
$775$	0.417887	−	1.60933i	0.0150109	−	0.0578087i
$776$			46.3777i			1.66486i
$777$	−23.6610	−	23.6610i	−0.848833	−	0.848833i
$778$	−3.34734	−	3.34734i	−0.120008	−	0.120008i
$779$	−58.7013			−2.10319
$780$	−5.49031	−	7.09803i	−0.196585	−	0.254150i
$781$		−	3.60541i		−	0.129012i
$782$	3.27531	−	9.78150i	0.117125	−	0.349786i
$783$	−10.8508	+	10.8508i	−0.387775	+	0.387775i
$784$			23.3098i			0.832494i
$785$	−25.2225	−	3.22130i	−0.900230	−	0.114973i
$786$	−29.6852			−1.05884
$787$	5.93878	−	5.93878i	0.211695	−	0.211695i	−0.593292	−	0.804987i	$-0.702172\pi$
$787$	5.93878	−	5.93878i	0.211695	−	0.211695i	0.804987	+	0.593292i	$0.202172\pi$
$788$	−30.6438	+	30.6438i	−1.09164	+	1.09164i
$789$	−16.2172			−0.577347
$790$	−10.0592	+	78.7629i	−0.357891	+	2.80226i
$791$	24.1496			0.858662
$792$	5.37948	−	5.37948i	0.191151	−	0.191151i
$793$	−6.53857	−	6.53857i	−0.232191	−	0.232191i
$794$			60.2754i			2.13909i
$795$	4.67278	+	6.04110i	0.165726	+	0.214256i
$796$			22.4135i			0.794424i
$797$	−24.8017	+	24.8017i	−0.878521	+	0.878521i	−0.993382	−	0.114860i	$-0.963358\pi$
$797$	−24.8017	+	24.8017i	−0.878521	+	0.878521i	0.114860	+	0.993382i	$0.463358\pi$
$798$	45.2192	−	45.2192i	1.60074	−	1.60074i
$799$	6.71095			0.237416
$800$	12.2686	−	7.21054i	0.433761	−	0.254931i
$801$			10.7083i			0.378357i
$802$	−22.5761	+	22.5761i	−0.797191	+	0.797191i
$803$	5.46171	+	5.46171i	0.192740	+	0.192740i
$804$	−33.2418			−1.17235
$805$	−19.6943	+	40.7557i	−0.694132	+	1.43645i
$806$	0.956277			0.0336834
$807$	15.9680	+	15.9680i	0.562101	+	0.562101i
$808$	−0.716547	+	0.716547i	−0.0252080	+	0.0252080i
$809$		−	17.2946i		−	0.608046i	−0.952665	−	0.304023i	$-0.901670\pi$
$809$		−	17.2946i		−	0.608046i	0.952665	−	0.304023i	$-0.0983300\pi$
$810$	−1.55506	+	12.1760i	−0.0546392	+	0.427821i
$811$	−26.4725			−0.929577			−0.464788	−	0.885422i	$-0.653870\pi$
$811$	−26.4725			−0.929577			−0.464788	+	0.885422i	$0.653870\pi$
$812$	35.9066	−	35.9066i	1.26007	−	1.26007i
$813$	13.4998	−	13.4998i	0.473458	−	0.473458i
$814$		−	18.2453i		−	0.639496i
$815$	24.4016	+	3.11646i	0.854751	+	0.109165i
$816$		−	1.76023i		−	0.0616203i
$817$	−39.0747	−	39.0747i	−1.36705	−	1.36705i
$818$	−7.31616	+	7.31616i	−0.255804	+	0.255804i
$819$	11.1161			0.388429
$820$	54.2719	−	41.9792i	1.89526	−	1.46598i
$821$	−43.7962			−1.52850			−0.764250	−	0.644921i	$-0.776890\pi$
$821$	−43.7962			−1.52850			−0.764250	+	0.644921i	$0.776890\pi$
$822$	23.3794	−	23.3794i	0.815449	−	0.815449i
$823$	33.3021	−	33.3021i	1.16084	−	1.16084i	0.176545	−	0.984293i	$-0.443508\pi$
$823$	33.3021	−	33.3021i	1.16084	−	1.16084i	0.984293	−	0.176545i	$-0.0564921\pi$
$824$	6.53020			0.227490
$825$	−3.40821	+	2.00308i	−0.118659	+	0.0697384i
$826$			59.6572i			2.07574i
$827$	−25.8943	+	25.8943i	−0.900432	+	0.900432i	−0.995473	−	0.0950413i	$-0.969702\pi$
$827$	−25.8943	+	25.8943i	−0.900432	+	0.900432i	0.0950413	+	0.995473i	$0.469702\pi$
$828$	12.2084	−	36.4596i	0.424272	−	1.26706i
$829$		−	47.9763i		−	1.66628i	−0.553059	−	0.833142i	$-0.686540\pi$
$829$		−	47.9763i		−	1.66628i	0.553059	−	0.833142i	$-0.313460\pi$
$830$	−26.5571	+	20.5419i	−0.921812	+	0.713019i
$831$	4.38960			0.152274
$832$	9.46636	+	9.46636i	0.328187	+	0.328187i
$833$	−6.90572	−	6.90572i	−0.239269	−	0.239269i
$834$			14.2260i			0.492608i
$835$	2.66541	−	20.8700i	0.0922405	−	0.722236i
$836$	22.5801			0.780951
$837$	1.10222	+	1.10222i	0.0380984	+	0.0380984i
$838$	30.0728	+	30.0728i	1.03885	+	1.03885i
$839$	17.5223			0.604937			0.302468	−	0.953159i	$-0.402189\pi$
$839$	17.5223			0.604937			0.302468	+	0.953159i	$0.402189\pi$
$840$	−4.31584	+	33.7927i	−0.148911	+	1.16596i
$841$	18.2831			0.630452
$842$	−8.28656	+	8.28656i	−0.285574	+	0.285574i
$843$	15.9488	+	15.9488i	0.549304	+	0.549304i
$844$			33.0084i			1.13620i
$845$	−20.4158	+	15.7916i	−0.702325	+	0.543247i
$846$	38.6282			1.32806
$847$	30.5514	−	30.5514i	1.04976	−	1.04976i
$848$	5.75339	+	5.75339i	0.197572	+	0.197572i
$849$	−18.0506			−0.619495
$850$	2.70292	−	10.4092i	0.0927095	−	0.357034i
$851$	−18.7437	−	37.6154i	−0.642526	−	1.28944i
$852$	−9.69728	−	9.69728i	−0.332223	−	0.332223i
$853$	16.3674	−	16.3674i	0.560411	−	0.560411i	−0.369013	−	0.929424i	$-0.620304\pi$
$853$	16.3674	−	16.3674i	0.560411	−	0.560411i	0.929424	+	0.369013i	$0.120304\pi$
$854$			77.0238i			2.63570i
$855$	−27.1275	+	20.9830i	−0.927740	+	0.717605i
$856$		−	32.9120i		−	1.12491i
$857$	16.3560	+	16.3560i	0.558709	+	0.558709i	0.928940	−	0.370231i	$-0.120721\pi$
$857$	16.3560	+	16.3560i	0.558709	+	0.558709i	−0.370231	+	0.928940i	$0.620721\pi$
$858$	−1.60772	−	1.60772i	−0.0548867	−	0.0548867i
$859$			10.2337i			0.349171i	0.984642	+	0.174585i	$0.0558585\pi$
$859$			10.2337i			0.349171i	−0.984642	+	0.174585i	$0.944141\pi$
$860$	64.0699	+	8.18270i	2.18477	+	0.279028i
$861$		−	31.8831i		−	1.08657i
$862$	20.8365	−	20.8365i	0.709695	−	0.709695i
$863$	23.0849	−	23.0849i	0.785819	−	0.785819i	−0.194986	−	0.980806i	$-0.562466\pi$
$863$	23.0849	−	23.0849i	0.785819	−	0.785819i	0.980806	+	0.194986i	$0.0624663\pi$
$864$			13.3412i			0.453878i
$865$	−29.1848	−	3.72735i	−0.992315	−	0.126734i
$866$		−	22.8331i		−	0.775900i
$867$	−10.3530	−	10.3530i	−0.351607	−	0.351607i
$868$	−3.64739	−	3.64739i	−0.123801	−	0.123801i
$869$			13.0281i			0.441948i
$870$	12.4780	−	9.65169i	0.423043	−	0.327223i
$871$		−	12.0706i		−	0.408995i
$872$	16.9069	−	16.9069i	0.572539	−	0.572539i
$873$	−17.9312	−	17.9312i	−0.606880	−	0.606880i
$874$	71.8879	−	35.8216i	2.43164	−	1.21168i
$875$	−17.5518	+	43.8063i	−0.593359	+	1.48092i
$876$	29.3801			0.992663
$877$	25.3709	+	25.3709i	0.856713	+	0.856713i	0.990949	−	0.134236i	$-0.0428581\pi$
$877$	25.3709	+	25.3709i	0.856713	+	0.856713i	−0.134236	+	0.990949i	$0.542858\pi$
$878$	29.8900	−	29.8900i	1.00874	−	1.00874i
$879$	−0.766711			−0.0258605
$880$	−3.33135	+	2.57679i	−0.112300	+	0.0868635i
$881$			42.4266i			1.42939i	0.699437	+	0.714694i	$0.253434\pi$
$881$			42.4266i			1.42939i	−0.699437	+	0.714694i	$0.746566\pi$
$882$	−39.7493	−	39.7493i	−1.33843	−	1.33843i
$883$	6.81198	−	6.81198i	0.229241	−	0.229241i	−0.583134	−	0.812376i	$-0.698174\pi$
$883$	6.81198	−	6.81198i	0.229241	−	0.229241i	0.812376	+	0.583134i	$0.198174\pi$
$884$	4.00540			0.134716
$885$	−1.52042	+	11.9048i	−0.0511083	+	0.400174i
$886$	−18.6973			−0.628148
$887$	10.3379	+	10.3379i	0.347114	+	0.347114i	0.859033	−	0.511919i	$-0.171065\pi$
$887$	10.3379	+	10.3379i	0.347114	+	0.347114i	−0.511919	+	0.859033i	$0.671065\pi$
$888$	−22.3659	−	22.3659i	−0.750552	−	0.750552i
$889$	−47.0394			−1.57765
$890$	3.31231	−	25.9351i	0.111029	−	0.869347i
$891$			2.01402i			0.0674722i
$892$	−6.75339	−	6.75339i	−0.226120	−	0.226120i
$893$	36.9490	+	36.9490i	1.23645	+	1.23645i
$894$	11.6801			0.390642
$895$	−24.8172	+	19.1960i	−0.829546	+	0.641652i
$896$		−	87.4862i		−	2.92271i
$897$	−4.96621	−	1.66292i	−0.165817	−	0.0555234i
$898$	31.1969	−	31.1969i	1.04106	−	1.04106i
$899$			1.08862i			0.0363076i
$900$	10.0749	−	38.7995i	0.335830	−	1.29332i
$901$	−3.40897			−0.113569
$902$	12.2927	−	12.2927i	0.409303	−	0.409303i
$903$	21.2231	−	21.2231i	0.706261	−	0.706261i
$904$	22.8278			0.759242
$905$	20.0930	−	15.5419i	0.667914	−	0.516630i
$906$	−24.3515			−0.809026
$907$	−2.11800	+	2.11800i	−0.0703271	+	0.0703271i	−0.741395	−	0.671068i	$-0.765836\pi$
$907$	−2.11800	+	2.11800i	−0.0703271	+	0.0703271i	0.671068	+	0.741395i	$0.265836\pi$
$908$	−16.6702	−	16.6702i	−0.553222	−	0.553222i
$909$		−	0.554084i		−	0.0183778i
$910$	−26.9230	−	3.43847i	−0.892488	−	0.113984i
$911$			14.9403i			0.494994i	0.968889	+	0.247497i	$0.0796081\pi$
$911$			14.9403i			0.494994i	−0.968889	+	0.247497i	$0.920392\pi$
$912$	9.69142	−	9.69142i	0.320915	−	0.320915i
$913$	−3.89530	+	3.89530i	−0.128916	+	0.128916i
$914$	20.3523			0.673196
$915$	−1.96302	+	15.3703i	−0.0648955	+	0.508127i
$916$		−	63.5807i		−	2.10077i
$917$	−41.1132	+	41.1132i	−1.35768	+	1.35768i
$918$	7.12926	+	7.12926i	0.235301	+	0.235301i
$919$	−21.5734			−0.711641			−0.355821	−	0.934554i	$-0.615799\pi$
$919$	−21.5734			−0.711641			−0.355821	+	0.934554i	$0.615799\pi$
$920$	−18.6164	+	38.5250i	−0.613763	+	1.27013i
$921$	8.42179			0.277508
$922$	−56.1213	−	56.1213i	−1.84826	−	1.84826i
$923$	3.52121	−	3.52121i	0.115902	−	0.115902i
$924$			12.2642i			0.403463i
$925$	−22.2012	−	37.7749i	−0.729970	−	1.24203i
$926$	−18.4187			−0.605275
$927$	−2.52480	+	2.52480i	−0.0829253	+	0.0829253i
$928$	−6.58830	+	6.58830i	−0.216271	+	0.216271i
$929$			49.0945i			1.61074i	0.592773	+	0.805370i	$0.298033\pi$
$929$			49.0945i			1.61074i	−0.592773	+	0.805370i	$0.701967\pi$
$930$	−0.980420	−	1.26752i	−0.0321492	−	0.0415635i
$931$		−	76.0427i		−	2.49220i
$932$	−1.72089	−	1.72089i	−0.0563697	−	0.0563697i
$933$	−5.27591	+	5.27591i	−0.172726	+	0.172726i
$934$	−43.7124			−1.43031
$935$	0.223544	−	1.75033i	0.00731067	−	0.0572420i
$936$	10.5077			0.343455
$937$	0.151208	−	0.151208i	0.00493975	−	0.00493975i	−0.704633	−	0.709572i	$-0.748888\pi$
$937$	0.151208	−	0.151208i	0.00493975	−	0.00493975i	0.709572	+	0.704633i	$0.248888\pi$
$938$	−71.0951	+	71.0951i	−2.32134	+	2.32134i
$939$	−18.8553			−0.615320
$940$	−60.5844	−	7.73755i	−1.97605	−	0.252371i
$941$			32.8976i			1.07243i	0.844081	+	0.536216i	$0.180147\pi$
$941$			32.8976i			1.07243i	−0.844081	+	0.536216i	$0.819853\pi$
$942$	−17.3283	+	17.3283i	−0.564587	+	0.564587i
$943$	12.7148	−	37.9719i	0.414051	−	1.23654i
$944$			12.7858i			0.416142i
$945$	−27.0687	−	34.9952i	−0.880545	−	1.13839i
$946$	16.3654			0.532085
$947$	28.4721	+	28.4721i	0.925220	+	0.925220i	0.997392	−	0.0721724i	$-0.0229932\pi$
$947$	28.4721	+	28.4721i	0.925220	+	0.925220i	−0.0721724	+	0.997392i	$0.522993\pi$
$948$	35.0410	+	35.0410i	1.13808	+	1.13808i
$949$			10.6683i			0.346308i
$950$	72.1926	−	42.4292i	2.34224	−	1.37659i
$951$	−25.2676			−0.819359
$952$	−10.7523	−	10.7523i	−0.348483	−	0.348483i
$953$	−27.1928	−	27.1928i	−0.880863	−	0.880863i	0.112760	−	0.993622i	$-0.464031\pi$
$953$	−27.1928	−	27.1928i	−0.880863	−	0.880863i	−0.993622	+	0.112760i	$0.964031\pi$
$954$	−19.6220			−0.635287
$955$	34.4054	−	26.6125i	1.11333	−	0.861160i
$956$	28.2254			0.912873
$957$	1.83022	−	1.83022i	0.0591628	−	0.0591628i
$958$	31.1385	+	31.1385i	1.00604	+	1.00604i
$959$		−	64.7596i		−	2.09120i
$960$	2.84201	−	22.2527i	0.0917255	−	0.718204i
$961$	−30.8894			−0.996433
$962$	17.8192	−	17.8192i	0.574513	−	0.574513i
$963$	12.7249	+	12.7249i	0.410055	+	0.410055i
$964$	−79.3443			−2.55551
$965$	−10.1891	−	1.30131i	−0.328000	−	0.0418906i
$966$	19.4562	+	39.0453i	0.625994	+	1.25626i
$967$	28.3587	+	28.3587i	0.911954	+	0.911954i	0.996426	−	0.0844721i	$-0.0269204\pi$
$967$	28.3587	+	28.3587i	0.911954	+	0.911954i	−0.0844721	+	0.996426i	$0.526920\pi$
$968$	28.8792	−	28.8792i	0.928214	−	0.928214i
$969$			5.74232i			0.184470i
$970$	37.8825	+	48.9755i	1.21633	+	1.57251i
$971$			19.8221i			0.636122i	0.948070	+	0.318061i	$0.103032\pi$
$971$			19.8221i			0.636122i	−0.948070	+	0.318061i	$0.896968\pi$
$972$	41.9590	+	41.9590i	1.34584	+	1.34584i
$973$	19.7027	+	19.7027i	0.631639	+	0.631639i
$974$			18.1155i			0.580458i
$975$	−5.28492	−	1.37231i	−0.169253	−	0.0439492i
$976$			16.5078i			0.528403i
$977$	31.2152	−	31.2152i	0.998663	−	0.998663i	−0.00133585	−	0.999999i	$-0.500425\pi$
$977$	31.2152	−	31.2152i	0.998663	−	0.998663i	0.999999	+	0.00133585i	$0.000425214\pi$
$978$	16.7643	−	16.7643i	0.536064	−	0.536064i
$979$		−	4.28990i		−	0.137106i
$980$	54.3806	+	70.3048i	1.73712	+	2.24580i
$981$			13.0736i			0.417407i
$982$	11.0755	+	11.0755i	0.353434	+	0.353434i
$983$	−34.0317	−	34.0317i	−1.08544	−	1.08544i	−0.995991	−	0.0894513i	$-0.971489\pi$
$983$	−34.0317	−	34.0317i	−1.08544	−	1.08544i	−0.0894513	−	0.995991i	$-0.528511\pi$
$984$		−	30.1381i		−	0.960767i
$985$	−3.34063	+	26.1569i	−0.106441	+	0.833427i
$986$			7.04129i			0.224240i
$987$	−20.0686	+	20.0686i	−0.638789	+	0.638789i
$988$	22.0528	+	22.0528i	0.701594	+	0.701594i
$989$	33.7398	−	16.8125i	1.07286	−	0.534606i
$990$	1.28672	−	10.0749i	0.0408946	−	0.320201i
$991$	−28.1825			−0.895246			−0.447623	−	0.894222i	$-0.647729\pi$
$991$	−28.1825			−0.895246			−0.447623	+	0.894222i	$0.647729\pi$
$992$	0.669240	+	0.669240i	0.0212484	+	0.0212484i
$993$	−3.12911	+	3.12911i	−0.0992993	+	0.0992993i
$994$	−41.4796			−1.31565
$995$	8.34411	+	10.7875i	0.264526	+	0.341987i
$996$			20.9540i			0.663952i
$997$	−19.7221	−	19.7221i	−0.624604	−	0.624604i	0.322101	−	0.946705i	$-0.395611\pi$
$997$	−19.7221	−	19.7221i	−0.624604	−	0.624604i	−0.946705	+	0.322101i	$0.895611\pi$
$998$	−27.3162	+	27.3162i	−0.864678	+	0.864678i
$999$	41.0775			1.29963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.e.a.22.2	yes	20
5.2	odd	4		575.2.e.d.68.10		20
5.3	odd	4	inner	115.2.e.a.68.1	yes	20
5.4	even	2		575.2.e.d.482.9		20
23.22	odd	2	inner	115.2.e.a.22.1	✓	20
115.22	even	4		575.2.e.d.68.9		20
115.68	even	4	inner	115.2.e.a.68.2	yes	20
115.114	odd	2		575.2.e.d.482.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.e.a.22.1	✓	20	23.22	odd	2	inner
115.2.e.a.22.2	yes	20	1.1	even	1	trivial
115.2.e.a.68.1	yes	20	5.3	odd	4	inner
115.2.e.a.68.2	yes	20	115.68	even	4	inner
575.2.e.d.68.9		20	115.22	even	4
575.2.e.d.68.10		20	5.2	odd	4
575.2.e.d.482.9		20	5.4	even	2
575.2.e.d.482.10		20	115.114	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68447 - 1.68447i) q^{2} +(-0.639677 + 0.639677i) q^{3} +3.67489i q^{4} +(1.36809 + 1.76871i) q^{5} +2.15503 q^{6} +(2.98466 - 2.98466i) q^{7} +(2.82130 - 2.82130i) q^{8} +2.18163i q^{9} +O(q^{10})\)	\(q+(-1.68447 - 1.68447i) q^{2} +(-0.639677 + 0.639677i) q^{3} +3.67489i q^{4} +(1.36809 + 1.76871i) q^{5} +2.15503 q^{6} +(2.98466 - 2.98466i) q^{7} +(2.82130 - 2.82130i) q^{8} +2.18163i q^{9} +(0.674828 - 5.28385i) q^{10} -0.873996i q^{11} +(-2.35074 - 2.35074i) q^{12} +(0.853585 - 0.853585i) q^{13} -10.0552 q^{14} +(-2.00654 - 0.256265i) q^{15} -2.15503 q^{16} +(0.638446 - 0.638446i) q^{17} +(3.67489 - 3.67489i) q^{18} +7.03028 q^{19} +(-6.49981 + 5.02758i) q^{20} +3.81844i q^{21} +(-1.47222 + 1.47222i) q^{22} +(-1.52277 + 4.54766i) q^{23} +3.60945i q^{24} +(-1.25665 + 4.83951i) q^{25} -2.87568 q^{26} +(-3.31457 - 3.31457i) q^{27} +(10.9683 + 10.9683i) q^{28} -3.27366i q^{29} +(2.94828 + 3.81163i) q^{30} -0.332539 q^{31} +(-2.01251 - 2.01251i) q^{32} +(0.559075 + 0.559075i) q^{33} -2.15089 q^{34} +(9.36229 + 1.19571i) q^{35} -8.01724 q^{36} +(-6.19651 + 6.19651i) q^{37} +(-11.8423 - 11.8423i) q^{38} +1.09204i q^{39} +(8.84986 + 1.13026i) q^{40} -8.34978 q^{41} +(6.43206 - 6.43206i) q^{42} +(-5.55806 - 5.55806i) q^{43} +3.21184 q^{44} +(-3.85866 + 2.98466i) q^{45} +(10.2255 - 5.09533i) q^{46} +(5.25569 + 5.25569i) q^{47} +(1.37853 - 1.37853i) q^{48} -10.8164i q^{49} +(10.2688 - 6.03521i) q^{50} +0.816798i q^{51} +(3.13683 + 3.13683i) q^{52} +(-2.66974 - 2.66974i) q^{53} +11.1666i q^{54} +(1.54584 - 1.19571i) q^{55} -16.8413i q^{56} +(-4.49711 + 4.49711i) q^{57} +(-5.51440 + 5.51440i) q^{58} -5.93299i q^{59} +(0.941746 - 7.37380i) q^{60} -7.66012i q^{61} +(0.560153 + 0.560153i) q^{62} +(6.51143 + 6.51143i) q^{63} +11.0901i q^{64} +(2.67753 + 0.341961i) q^{65} -1.88349i q^{66} +(7.07050 - 7.07050i) q^{67} +(2.34622 + 2.34622i) q^{68} +(-1.93495 - 3.88311i) q^{69} +(-13.7564 - 17.7847i) q^{70} +4.12520 q^{71} +(6.15503 + 6.15503i) q^{72} +(-6.24912 + 6.24912i) q^{73} +20.8757 q^{74} +(-2.29187 - 3.89957i) q^{75} +25.8355i q^{76} +(-2.60859 - 2.60859i) q^{77} +(1.83951 - 1.83951i) q^{78} -14.9063 q^{79} +(-2.94828 - 3.81163i) q^{80} -2.30438 q^{81} +(14.0650 + 14.0650i) q^{82} +(-4.45689 - 4.45689i) q^{83} -14.0323 q^{84} +(2.00268 + 0.255772i) q^{85} +18.7248i q^{86} +(2.09409 + 2.09409i) q^{87} +(-2.46581 - 2.46581i) q^{88} +4.90838 q^{89} +(11.5274 + 1.47222i) q^{90} -5.09533i q^{91} +(-16.7121 - 5.59601i) q^{92} +(0.212718 - 0.212718i) q^{93} -17.7061i q^{94} +(9.61807 + 12.4345i) q^{95} +2.57472 q^{96} +(-8.21920 + 8.21920i) q^{97} +(-18.2200 + 18.2200i) q^{98} +1.90673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Introduction

L-functions

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